Problem: $70$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $50$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 70}$ ${x = 3y-50}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-50}$ for $x$ in the first equation. ${(3y-50)}{+ y = 70}$ Simplify and solve for $y$ $ 3y-50 + y = 70 $ $ 4y-50 = 70 $ $ 4y = 120 $ $ y = \dfrac{120}{4} $ ${y = 30}$ Now that you know ${y = 30}$ , plug it back into ${x = 3y-50}$ to find $x$ ${x = 3}{(30)}{ - 50}$ $x = 90 - 50$ ${x = 40}$ You can also plug ${y = 30}$ into ${x+y = 70}$ and get the same answer for $x$ ${x + }{(30)}{= 70}$ ${x = 40}$ There were $40$ home team fans and $30$ away team fans.